Given the first four terms of an arithmetic sequence find the rule

The video tutorial explains how to find the formula for an arithmetic sequence. It begins by converting terms to fractions to simplify subtraction and identify the common difference. The common difference is found to be -5/2. The tutorial then applies the arithmetic sequence formula, a_n = a_1 + (n-1) * d, and finalizes it by combining terms to get the formula a_n = -5/2n + 13/2.

What is the first step in finding the common difference in an arithmetic sequence?

• Add all terms together

• Convert terms to have a common denominator

• Multiply all terms by 2

• Divide each term by 2

What is the common difference in the given sequence?

• 3/2

• -5/2

• 7/2

• 2/2

Which formula represents the nth term of an arithmetic sequence?

• a_n = a_1 - n * d

• a_n = a_1 * n + d

• a_n = a_1 / (n + d)

• a_n = a_1 + (n - 1) * d

What is the result of applying the distributive property to the formula for the nth term?

• a_n = 4 + 5/2

• a_n = 4 - 5/2 * n + 5/2

• a_n = 4 * 5/2 * n

• a_n = 4 / 5/2

What is the final expression for the nth term after combining terms?

• a_n = -5/2 * n + 13/2

• a_n = -5/2 + 13/2

• a_n = 5/2 * n + 13/2

• a_n = 5/2 + 13/2